Was told by Tech support that my motherboard died and that to retrieve data from my hard drive I would need to replace it with the same motherboard. Is this true? How else can I get the data off the hard drive? Can't I just plug the drive into another computer as a second drive and get the info?
As far as data recovery is concerned, what a crock. Slave the drive in another box following muno's admonition re file systems and you can recover your data.
If you plan to use the drive, intact, as a master on a new (different) motherboard then you could run into problems.
It might and very well may happen that the old and new mainboards do not come to agree on the drive's (virtual) geometry. In that case, it stays inaccessible.
So the shop's recommendation to plug it onto the exact same type of mainboard isn't actually that far off. If I had to play safe on a customer's sole copy of important data, that'd be what I'd do.